基于模拟的T20板球击打顺序和保龄球计划的优化

Simulation-Based Optimisation of Batting Order and Bowling Plans in T20 Cricket

This paper develops a unified Markov Decision Process (MDP) framework for optimising two recurring in-match decisions in T20 cricket namely batting order selection and bowling plan assignment, directly in terms of win and defend probability rather than expected runs. A three-phase player profile engine (Powerplay, Middle, Death) with James-Stein shrinkage is estimated from 1,161 IPL ball-by-ball records (2008-2025). Win/defend probabilities are evaluated by vectorised Monte Carlo simulation over N = 50,000 innings trajectories. Batting orders are searched by exhaustive enumeration. Bowling plans are computed by simulated annealing over the remaining quota with the constraint that the same bowler cannot bowl consecutive overs. Applied to two 2026 IPL matches, the optimal batting order improves Mumbai Indians' win probability by 4.1 percentage points (52.4% to 56.5%), and the optimal Gujarat Titans bowling plan improves defend probability by 5.2 percentage points (39.1% to 44.3%). In both cases the observed sub-optimality is consistent with phase-agnostic deployment in decisions that appear reasonable by aggregate metrics but are exposed as costly when phase-specific profiles are applied.